+C$_{\text{i}}$ pairs of the \hkl<1 0 0>-type have been considered in the first part.\r
+Fig.~\ref{fig:combos_ci} schematically displays the position of the initial C$_{\text{i}}$ \hkl[0 0 -1] DB and the various positions for the second defect (1-5) used for investigating the defect pairs.\r
+Table~\ref{table:dc_c-c} summarizes the binding energies for the combination with a second C-Si \hkl<1 0 0> DB obtained for different orientations.\r
+\begin{figure}\r
+%\begin{minipage}{0.49\columnwidth}\r
+\subfigure[]{\label{fig:combos_ci}\includegraphics[width=0.45\columnwidth]{combos_ci.eps}}\r
+\hspace{0.1cm}\r
+\subfigure[]{\label{fig:combos_si}\includegraphics[width=0.45\columnwidth]{combos.eps}}\r
+\caption{Positions of the initial C$_{\text{i}}$ \hkl[0 0 -1] DB (I) (Fig.~\ref{fig:combos_ci}), the lattice site chosen for the initial Si$_{\text{i}}$ \hkl<1 1 0> DB (Si$_{\text{i}}$) occupying various orientations (Fig.~\ref{fig:combos_si}) and neighbored positions (1-5) for the second defect used for investigating defect pairs.} \r
+\label{fig:combos}\r
+\end{figure}\r
+\begin{table}\r
+\begin{ruledtabular}\r
+\begin{tabular}{l c c c c c c }\r
+ & 1 & 2 & 3 & 4 & 5 & R \\\r
+\hline\r
+ \hkl[0 0 -1] & -0.08 & -1.15 & -0.08 & 0.04 & -1.66 & -0.19\\\r
+ \hkl[0 0 1] & 0.34 & 0.004 & -2.05 & 0.26 & -1.53 & -0.19\\\r
+ \hkl[0 -1 0] & -2.39 & -0.17 & -0.10 & -0.27 & -1.88 & -0.05\\\r
+ \hkl[0 1 0] & -2.25 & -1.90 & -2.25 & -0.12 & -1.38 & -0.06\\\r
+ \hkl[-1 0 0] & -2.39 & -0.36 & -2.25 & -0.12 & -1.88 & -0.05\\\r
+ \hkl[1 0 0] & -2.25 & -2.16 & -0.10 & -0.27 & -1.38 & -0.06\\\r
+\end{tabular}\r
+\end{ruledtabular}\r
+\caption{Binding energies of C$_{\text{i}}$ \hkl<1 0 0>-type defect pairs in eV. Equivalent configurations exhibit equal energies. The first column lists the orientation of the defect, which is combined with the initial C$_{\text{i}}$ \hkl[0 0 -1] dumbbell. The position index of the second defect is given in the first row according to Fig.~\ref{fig:combos}. R corresponds to the position located at $\frac{a_{\text{Si}}}{2}\hkl[3 2 3]$ relative to the initial defect position, which is the maximum realizable distance due to periodic boundary conditions.}\r
+\label{table:dc_c-c}\r
+\end{table}\r
+Most of the obtained configurations result in binding energies well below zero indicating a preferable agglomeration of these type of defects.\r
+For increasing distances of the defect pair the binding energy approaches to zero (R in Table~\ref{table:dc_c-c}) as it is expected for non-interacting isolated defects.\r
+Energetically favorable and unfavorable configurations can be explained by stress compensation and increase respectively based on the resulting net strain of the respective configuration of the defect combination.\r
+Antiparallel orientations of the second defect (\hkl[0 0 1]) at positions located below the \hkl(0 0 1) plane with respect to the initial one (positions 1, 2 and 4) show the energetically most unfavorable configurations.\r
+In contrast, the parallel and particularly the twisted orientations constitute energetically favorable configurations, in which a vast reduction of strain is enabled by combination of these defects.\r
+\r
+Mattoni et al.\cite{mattoni2002} predict the ground state configuration for a \hkl[1 0 0] or equivalently a \hkl[0 1 0] defect created at position 1 with both defects basically maintaining the DB structure, resulting in a binding energy of \unit[-2.1]{eV}.\r
+In this work we found a further relaxation of this defect structure.\r
+The C atom of the second and the Si atom of the initial DB move towards each other forming a bond, which results in a somewhat lower binding energy of \unit[-2.25]{eV}.\r
+Furthermore a more favorable configuration was found for the combination with a \hkl[0 -1 0] and \hkl[-1 0 0] DB respectively, which is assumed to constitute the actual ground state configuration of two C$_{\text{i}}$ DBs in Si.\r
+The atomic arrangement is shown in the bottom right of Fig.~\ref{fig:036-239}.\r
+The two C atoms form a strong C-C bond, which is responsible for the large gain in energy resulting in a binding energy of \unit[-2.39]{eV}.\r
+\r
+Investigating migration barriers enables to predict the probability of formation of defect complexes by thermally activated diffusion processes.\r
+% ground state configuration, C cluster\r
+Based on the lowest energy migration path of a single C$_{\text{i}}$ DB the configuration, in which the second C$_{\text{i}}$ DB is oriented along \hkl[0 1 0] at position 2 is assumed to constitute an ideal starting point for a transition into the ground state.\r
+In addition, the starting configuration exhibits a low binding energy (\unit[-1.90]{eV}) and is, thus, very likely to occur.\r
+However, a barrier height of more than \unit[4]{eV} was detected resulting in a low probability for the transition.\r
+The high activation energy is attributed to the stability of such a low energy configuration, in which the C atom of the second DB is located close to the initial DB.\r
+Low barriers have only been identified for transitions starting from energetically less favorable configurations, e.g. the configuration of a \hkl[-1 0 0] DB located at position 2 (\unit[-0.36]{eV}).\r
+Starting from this configuration, an activation energy of only \unit[1.2]{eV} is necessary for the transition into the ground state configuration.\r
+The corresponding migration energies and atomic configurations are displayed in Fig.~\ref{fig:036-239}.\r
+\begin{figure}\r
+\includegraphics[width=\columnwidth]{036-239.ps}\r
+\caption{Migration barrier and structures of the transition of a C$_{\text{i}}$ \hkl[-1 0 0] DB at position 2 (left) into a C$_{\text{i}}$ \hkl[0 -1 0] DB at position 1 (right). An activation energy of \unit[1.2]{eV} is observed.}\r
+\label{fig:036-239}\r
+\end{figure}\r
+% strange mig from -190 -> -2.39 (barrier > 4 eV)\r
+% C-C migration -> idea:\r
+% mig from low energy confs has extremely high barrier!\r
+% low barrier only from energetically less/unfavorable confs (?)! <- prove!\r
+% => low probability of C-C clustering ?!?\r
+%\r
+% should possibly be transfered to discussion section\r
+Since thermally activated C clustering is, thus, only possible by traversing energetically unfavored configurations, mass C clustering is not expected.\r
+Furthermore, the migration barrier of \unit[1.2]{eV} is still higher than the activation energy of \unit[0.9]{eV} observed for a single C$_{\text{i}}$ \hkl<1 0 0> DB in c-Si.\r
+The migration barrier of a C$_{\text{i}}$ DB in a complex system is assumed to approximate the barrier of a DB in a separated system with increasing defect separation.\r
+Thus, lower migration barriers are expected for pathways resulting in larger separations of the C$_{\text{i}}$ DBs.\r
+% calculate?!? ... hopefully acknowledged by 188-225 calc\r
+However, if the increase of separation is accompanied by an increase in binding energy, this difference is needed in addition to the activation energy for the respective migration process.\r
+Configurations, which exhibit both, a low binding energy as well as afferent transitions with low activation energies are, thus, most probable C$_{\text{i}}$ complex structures.\r
+On the other hand, if elevated temperatures enable migrations with huge activation energies, comparably small differences in configurational energy can be neglected resulting in an almost equal occupation of such configurations.\r
+In both cases the configuration yielding a binding energy of \unit[-2.25]{eV} is promising.\r
+First of all, it constitutes the second most energetically favorable structure.\r
+Secondly, a migration path with a barrier as low as \unit[?.?]{eV} exists starting from a configuration of largely separated defects exhibiting a low binding energy (\unit[-1.88]{eV}).\r
+The migration barrier and correpsonding structures are shown in Fig.~\ref{fig:188-225}.\r
+% 188 - 225 transition in progress\r
+\begin{figure}\r
+\includegraphics[width=\columnwidth]{188-225.ps}\r
+\caption{Migration barrier and structures of the transition of a C$_{\text{i}}$ \hkl[0 -1 0] DB at position 5 (left) into a C$_{\text{i}}$ \hkl[1 0 0] DB at position 1 (right). An activation energy of \unit[?.?]{eV} is observed.}\r
+\label{fig:188-225}\r
+\end{figure}\r
+Finally, this type of defect pair is represented four times (two times more often than the ground state configuration) within the systematically investigated configuration space.\r
+The latter is considered very important for high temperatures, which is accompanied by an increase in the entropic contribution to structure formation.\r
+Thus, C agglomeration indeed is expected but only a low probability is assumed for C clustering by thermally activated processes with regard to the considered period of time.\r
+% ?!?\r
+% look for precapture mechnism (local minimum in energy curve)\r
+% also: plot energy all confs with respect to C-C distance\r
+% maybe a pathway exists traversing low energy confs ?!?\r
+\r
+% point out that configurations along 110 were extended up to the 6th NN in that direction\r
+The binding energies of the energetically most favorable configurations with the seocnd DB located along the \hkl[1 1 0] direction and resulting C-C distances of the relaxed structures are summarized in Table~\ref{table:dc_110}.\r
+\begin{table}\r
+\begin{ruledtabular}\r
+\begin{tabular}{l c c c c c c }\r
+ & 1 & 2 & 3 & 4 & 5 & 6 \\\r
+\hline\r
+ $E_{\text{b}}$ [eV] & -2.39 & -1.88 & -0.59 & -0.31 & -0.24 & -0.21 \\\r
+C-C distance [nm] & 0.14 & 0.46 & 0.65 & 0.86 & 1.05 & 1.08 \r
+\end{tabular}\r
+\end{ruledtabular}\r
+\caption{Binding energies $E_{\text{b}}$ and C-C distance of energetically most favorable C$_{\text{i}}$ \hkl<1 0 0>-type defect pairs separated along bonds in the \hkl[1 1 0] direction.}\r
+\label{table:dc_110}\r
+\end{table}\r
+The binding energy of these configurations with respect to the C-C distance is plotted in Fig.~\ref{fig:dc_110}\r
+\begin{figure}\r
+\includegraphics[width=\columnwidth]{db_along_110_cc_n.ps}\r
+\caption{Minimum binding energy of dumbbell combinations separated along \hkl[1 1 0] with respect to the C-C distance. The blue line is a guide for the eye and the green curve corresponds to the most suitable fit function consisting of all but the first data point.}\r
+\label{fig:dc_110}\r
+\end{figure}\r
+The interaction is found to be proportional to the reciprocal cube of the C-C distance for extended separations of the C$_{\text{i}}$ and saturates for the smallest possible separation, i.e. the ground state configuration.\r
+Not considering the previously mentioned elevated barriers for migration an attractive interaction between the C$_{\text{i}}$ defects indeed is detected with a capture radius that clearly exceeds the \unit[1]{nm} mark.\r
+The interpolated graph suggests the disappearance of attractive interaction forces, which are proportional to the slope of the graph, inbetween the two lowest separation distances of the defects.\r
+This finding, in turn, supports the previously established assumption of C agglomeration and absence of C clsutering.\r